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A minor arc is an arc that measures less than 180. A major arc is an arc that measures greater than 180. A semicircle is an arc with endpoints that lie on a diameter.
Type: Semicircle
Measure: 180^(∘)
An arc is a portion of a circle defined by two endpoints. A central angle separates the circle into two arcs — the major arc and the minor arc. The measures of these arcs are related to the measure of the central angle.
Arc | Measure |
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A minor arc is the shortest arc connecting two endpoints on a circle. | The measure is less than 180 and is equal to the measure of its related central angle.
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A major arc is the longest arc connecting two endpoints on a circle. | The measure is greater than 180 and is equal to 360 minus the measure of the minor arc with the same endpoints.
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A semicircle is an arc with endpoints that lie on a diameter. | The measure of a semicircle is 180.
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The arc that we are looking at is RST. It is the arc that connects the endpoints R and T in counterclockwise direction. To find its measure, we first need to find the measure of the arc, RPT, the arc that connect the same endpoints in the clockwise direction. mRPT=mRQ+mQP+mPT ⇓ mRPT= 25+ 65+ 90=180 Now we will use that the measures of RST and RPT add to 360. m RST+mRPT=360 ⇓ m RST=360-mRPT=360-180=180 Since the measure of RST is 180 it is a semicircle.